Graphics Programs Reference
In-Depth Information
Scaling: If
Fx
({}
X
()
=
then
4.
-----
X
ω
1
a
---
Fxa
()
{
}
=
(13.13)
Central Ordinate:
5.
∞
∫
X
()
=
x
()
d
(13.14)
∞
∞
∫
1
2π
x
()
=
------
X
()ω
d
(13.15)
∞
Frequency Shift: If
Fx
({}
X
()
=
then
6.
Fe
ω
0
t
±
−
{
x
()
}
=
X
ωω
0
(
)
(13.16)
Modulation: If
Fx
({}
X
()
=
then
7.
1
---
X
ωω
0
Fx
() ω
0
t
{
cos
}
=
[
(
+
)
+
X
ωω
0
(
)
]
(13.17)
1
2
j
-----
X
ωω
0
Fx
() ω
0
t
{
sin
(
)
}
=
[
(
) ωω
0
(
+
)
]
(13.18)
Derivatives:
8.
n
d
j
(
n
X
()
F
(
x
()
)
=
(13.19)
t
n
d
Time Convolution: if
x
()
and
h
()
have Fourier transforms
X
()
and
9.
H
()
, respectively, then
∞
∫
Fx
()
ht
τ
(
) τ
d
=
X
()
H
()
(13.20)
∞
10.
Frequency Convolution:
∞
∫
1
2π
Fx
()
h
()
{
}
=
------
X
()
H
ωτ
(
)
d
(13.21)
∞
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